On Second-Order Differentiability with Respect to Parameters for Differential Equations with State-Dependent Delays

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Abstract

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone.

Original languageEnglish
Pages (from-to)1089-1138
Number of pages50
JournalJournal of Dynamics and Differential Equations
Volume25
Issue number4
DOIs
Publication statusPublished - Nov 15 2013

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Keywords

  • Delay differential equation
  • Differentiability with respect to parameters
  • State-dependent delay

ASJC Scopus subject areas

  • Analysis

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